Frequency selective electrical filters for communications applications were developed beginning around 1910, for telegraphy and telephony uses, particularly for multiplexing and de-multiplexing of communication signal channels carried on long distance cables and wireless links. Later they were used for many other applications. Filter design methods, named “image” or “image parameter” design methods, were developed by G. A. Campbell (Campbell 1922) and A. Zobel (Zobel 1924) of Bell Telephone Laboratories, among others. These filter circuits utilized circuit elements including inductors, capacitors, and transformers. In the 1920's, a new circuit element began to be used in some electrical signal filters, the acoustic wave (AW) resonator, specifically the quartz bulk acoustic wave resonator; whose electrical circuit equivalent was first described by Van Dyck (Van Dyck 1928); its equivalent circuit has two resonances closely spaced in frequency, the “resonance” and the “anti-resonance”. The image filter design methods were applied to filter circuits utilizing these quartz resonators, and two acoustic wave filter circuit types resulted, “ladder” and “lattice” acoustic wave filter designs (Mason 1934). Beginning ˜1990 thin film surface acoustic wave (SAW) resonators and bulk acoustic wave resonators (BAW) were developed and began to be used in microwave AW ladder filter designs. The image designed acoustic wave ladder bandpass filter in SAW and BAW implementations is often used for microwave filtering applications in the RF frontend of mobile communications devices. These filters meet the demanding requirements: microwave frequencies (>˜500 MHz), low insertion loss, high selectivity, small circuit area, high power handling, high linearity, and low cost. The traditional AW ladder filter is often preferred because it satisfies these requirements (Morgan 2007). Minor variations to the traditional AW ladder have also been considered for these applications (Taiyo Yuden 2011 etc.), which typically add one or more circuit elements (capacitor, inductor, AW resonator) to the ladder design to enhance a particular circuit feature. This can be done when the influences to the basic AW ladder circuit are minor enough that common computer optimization tools converge. This is a stringent requirement for any circuit containing closely spaced series and parallel resonances like the AW ladder filter, and thus permits only very minor variations to the basic AW ladder design and function.
In the 1920's and 1930's another approach was developed for the design of frequency selective electrical signal filters for communications applications—“network synthesis”. This new filter circuit design method was pioneered by Foster and Darlington (Foster 1922, Darlington 1938) in the U.S. and Cauer (Cauer 1933 and 1940) in Germany, among others. In “network synthesis” the desired filter response is translated into a ratio of polynomials, termed a rational function, and a filter circuit is “synthesized” from this function. Neglecting losses, which are kept small in practice, the “synthesized” circuit matches the desired response function. In the 1950's and 1960's, network synthesis was successfully applied to the design of microwave filters for communications and other applications. These new filters utilize high Q (low loss) electromagnetic resonators and electromagnetic couplings between these resonators as circuit elements. (Matthaei 1964, Cameron 2007).